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Library / First Principles Framework (FPF) - Core Conceptual Specification
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C.22.2:10 - Structure Cue That Improves Formulation

C.29 carries mathematical-lens use for first-principles or mathematical structure cues used by ProblemCard.

firstPrinciplesCue is a local cue label for a formulation-changing structure and a cue to apply C.29; it is not a local mathematical-lens kind or a substitute for a C.29 lens-use result.

The problem card may ask whether a first-principles or mathematical structure helps find or improve the problem formulation, not only whether an already-mentioned mathematical expression helps the problem formulation. Useful cues include state space, graph, boundary, topology, symmetry, invariant, variational or constrained-optimization structure, probability or information structure, resource bound, obstruction, scale window, composition, or coarse-graining choice.

The practitioner-facing use is:

State the structure that improves the problem formulation, the preserved structure, the lost structure, the practical payoff, the problem-formulation follow-up reason, and the stop condition.

Distribution by principles:

Source-side cueCurrent FPF pattern or relationC.22.2 use
Zero-principles and first-principles invariants, constraints, symmetry, composition, multi-scale description, variational structure, probability or information, and resource limitsC.29, with A.19, C.16, C.25, and G.9 when characteristics, measurement characterization, quality bundles, or parity are currentCarry a first-principles or mathematical structure cue and apply the subject pattern for the claim being made, relation, or boundary.
Second-principles method-family implicationsG.5, A.15, E.18, A.19 as applicableName the method-family cue; do not perform method selection in the problem card.
Third-principles reproducibility, checks, templates, records, logs, rollback, evidenceA.10, G.6, B.3, A.21, G.11, E.16 as applicableName the reproducibility or evidence cue and apply the subject pattern for the claim kind named by value before relying on that claim.

When no useful mathematical structure survives, record that absence and proceed without forcing mathematical prose into the problem card.